Mathematical Modeling of Honeybee Population Dynamics

Honeybees are important pollinators worldwide and pollinate about one-third of the food we consume. Recently though, honeybee colonies have been under increasing stress due to changing environments, pesticides, mites, and viruses, which has increased the incidence of
colony collapse. This paper aims to understand how these different factors contribute to the decline of honeybee populations by using two separate approaches: data analysis and mathematical modeling. The data analysis examines the relative impacts of mites, pollen, mites, and viruses on honeybee populations and colony collapse. From the data, low initial bee populations lead to collapse in September while mites and viruses can lead to collapse in December. Feeding bee colonies also has a mixed effect, where it increases both bee and mite populations. For the model, we focus on the population dynamics of the honeybee-mite interaction. Using a system of delay differential equations with five population components, we find that bee colonies can collapse from mites, coexist with mites, and survive without them. As long as bees produce more pupa than the death rate of pupa and mites produce enough phoretic mites compared to their death rates, bees and mites can coexist. Thus, it is possible for honeybee colonies to withstand mites, but if the parasitism is too large, the colony will collapse. Provided
this equilibrium exists, the addition of mites leads to the colony moving to the interior equilibrium. Additionally, population oscillations are persistent if they occur and are connected to the interior equilibrium. Certain parameter values destabilize bee populations, leading to large
oscillations and even collapse. From these parameters, we can develop approaches that can help us prevent honeybee colony collapse before it occurs.